GG 711: Advanced Techniques in Geophysics and Materials Science

Pavel Zinin HIGP, University of Hawaii, Honolulu, USA

Nano-Microscopy. Lecture 2

Scanning and Transmission Electron Microscopies:

Principles

www.soest.hawaii.edu\~zinin

Why Electrons

0.61 0.61

sinAiryr

n nNA

It all started with light, but even with better lenses, oil immersion and short wavelengths, resolution

was only about 0.2 mm/1000x = 0.2 m.

1 cm 1 mm 1 µm 1 nm 1 Å

AFM

STM SAM

SEM

OM

Black Body Radiation

Sketch of the black body: The opening in the cavity of a body is a

good approximation to a black body. As light enters the cavity

through the small opening, part is reflected and part is absorbed on

each reflection from the interior walls. After many reflections,

essentially all of the incident energy is absorbed.

A black body is an idealized physical body that

absorbs all incident electromagnetic radiation.

Because of this perfect absorptivity at all

wavelengths, a black body is also the best possible

emitter of thermal radiation, which it radiates

incandescently in a characteristic, continuous

spectrum that depends on the body's temperature.

At Earth-ambient temperatures this emission is in

the infrared region of the electromagnetic

spectrum and is not visible. The object appears

black, since it does not reflect or emit any visible

light.

The color (chromaticity) of blackbody radiation depends on the

temperature of the black body; the locus of such colors, shown

here in CIE 1931 x,y space, is known as the Planckian locus

(Wikipedia, 2011).

Black Body Radiation

An object at any temperature is

known to emit radiation sometimes

referred to as thermal radiation. The

characteristics of this radiation

depend on the temperature and

properties of the object. At low

temperatures, the wavelengths of the

thermal radiation are mainly in the

infrared region and hence are not

observed by the eye. As the

temperature of the object is increased,

it eventually begins to glow red. At

sufficiently high temperatures, it

appears to be white, as in the glow of

the hot tungsten filament of a light

bulb. A careful study of thermal

radiation shows that it consists of a

continuous distribution of

wavelengths from the infrared,

visible, and ultraviolet portions of the

spectrum.

As the temperature decreases, the peak of the

blackbody radiation curve moves to lower intensities

and longer wavelengths. The blackbody radiation graph

is also compared with the classical model of Rayleigh

and Jeans.

Planck Postualte

nhE

Max Planck (1858- 1947).

Nobel Prize in Physics

(1918.)

The Planck Postulate (or Planck's Postulate), one of the

fundamental principles of quantum mechanics, is the

postulate that the energy of oscillators in a black body is

quantized, and is given by

where n is an integer 1, 2, 3, ..., h is Planck's constant,

and (the Greek letter) is the frequency of the

oscillator. The energies of the molecule are said to be

quantized, and the allowed energy states are called

quantum states. The factor h is a constant, known as

Planck's constant, given by : h = 6.626 X 10-34 J. s

2. The molecules emit energy in discrete units of light

energy called quanta (or photons, as they are now

called).

In his theory, Planck made two assumptions:

1. The vibrating molecules that emitted the radiation

could have only certain discrete amounts of energy, En,

given by

Application Black Body Radiation Theory

1exp 25

1

T

c

cI

1ln TJ

Temperature is calculated from the

radiation emitted from a material using

Planck's blackbody equation:

where I is spectral intensity, is emissivity, is

wavelength, c1 and c2 are physical constants, and T

is temperature.

J = ln(I5/c1) and = c2/.

Temperature can also be calculated using

Wien's approximation to Planck's law:

Thus. a linear fit to a spectrum transformed to

coordinates of J and yields both temperature

(inverse slope) and emissivity (y-intercept).

Wien's approximation and Planck's law give

nearly identical temperatures up to about 3000 K,

but diverge at higher temperatures with Wien's

law giving progressively lower values (~ 1 at

5000 K).

The Wave Properties of Particles

In 1924, the French physicist Louis de Broglie wrote a doctoral

dissertation. “"The fundamental idea of [my 1924 thesis] was the

following: The fact that, following Einstein's introduction of

photons in light waves, one knew that light contains particles

which are concentrations of energy incorporated into the wave,

suggests that all particles, like the electron, must be transported

by a wave into which it is incorporated... My essential idea was

to extend to all particles the coexistence of waves and particles

discovered by Einstein in 1905 in the case of light and photons."

"With every particle of matter with mass m and velocity v a real

wave must be 'associated'", related to the momentum by the

equation:

mv

h

p

h

From CHEM 793, 2008 Fall

Where is the wavelength of particle, h is the Planck's

const, m is the particle mass, and v is the particle velocity.

http://www.youtube.com/watch?v=DfPeprQ7oGc

Why Electrons

An electron microscope is an instrument that uses electrons instead of light for the

imaging of objects. The development of the transmission electron microscope was

based on theoretical work done by Louis de Broglie, discovered that moving

particles have a wave nature. Louis de Broglie found that wavelength of moving

particle is inversely proportional to momentum, p:

mv

h

p

h

From CHEM 793, 2008 Fall

Where is the wavelength of particle, h is the Planck's

const, m is the particle mass, and v is the particle velocity.

Louis-Victor-Pierre-

Raymond, 7th duc de Broglie

(1892 – 1987). Nobel Prize in

Physics (1929)

http://www.youtube.com/watch?v=DfPeprQ7oGc

Why Electrons

An electron accelerated in a potential of V volts has kinetic energy m×v2/2 = e V where

e is the charge on the electron. Solving for v and substituting into de Broglie's equation

(and expanding in V to account for the fact that the electron mass is different when

moving than when at rest):

mv

h

p

h

22

2

eV hv

m m e V

eVmv 2

2

1

So the momentum is

Electrons have a charge and can be accelerated in an electric potential field as well as

focused by electric or magnetic fields. If an electron is accelerated through a potential

eV, it gains kinetic energy

Where V (in Volts)is the electrical potential.

meVmv 2

Resolution of SEM

VmeV

h 2.12

2

2

Å

Substitutin the known values in this equation: h = 6.6 10-27; m = 9.1 10-28;

e = 4.8 10-10; e.s.u. We obtain:

VnnrAiry

sin

3.1261.0

sin

61.0

Then, for the Airy radius we have

Since electron microscope aperture angles are always very small sin, and since the

object and image are in field free space in SEM, the refraction index n = 1. Thus

VrAiry

5.7 =10-2 radians, V=105 volts

r ~ 2.4 Å (Wischnitzer, 1970)

Resolution of SEM

Electron Microscopy

Definition: The scanning electron microscope

(SEM) is a type of electron microscope that

images the sample surface by scanning it with

a high-energy beam of electrons in a raster

scan pattern.

The electrons interact with the atoms that

make up the sample producing signals that

contain information about the sample's

surface topography, composition and other

properties such as electrical (Wikipedia,

2009).

Electron microscopes have much greater

resolving power than light microscopes that

use electromagnetic radiation and can obtain

much higher magnifications of up to 2 million

times, while the best light microscopes are

limited to magnifications of 2000 times.

Resolving power line

Scanning Electron Microscopy (SEM) Instrumentation - How Does It Work?

Essential components of all SEMs include the following:

1.Electron Source ("Gun")

2.Electron Lenses

3.Sample Stage

4.Detectors for all signals of interest

5.Display / Data output devices

6.Infrastructure Requirements:

a. Power Supply

b. Vacuum System

c. Cooling system

d. Vibration-free floor

e. Room free of ambient magnetic and electric fields

SEMs always have at least one detector (usually a secondary electron detector), and

most have additional detectors. The specific capabilities of a particular instrument are

critically dependent on which detectors it accommodates.

Source of Electrons

An electron gun (also called electron emitter) is an electrical component that produces an

electron beam that has a precise kinetic energy and is most often used in televisions and

monitors which use cathode ray tube technology, as well as in other instruments, such as

electron microscopes and particle accelerators (Wikipedia, 2009).

Principle:

•A voltage is applied to a tungsten filament (cathode): it is heated and electrons are produced

•The electrons are accelerated to the anode.

•Electrons can exit a small (<1mm) hole to move down the EM column (in a vacuum) for

imaging

The Filament & Thermionic Emission

Tungsten wire

The tungsten cathode is a fine wire

approximately 100mm in diameter

that has been bent into the shape of a

hairpin with a V-shaped tip. The tip is

heated by passing current through it;

normally, the tip is heated to around

2400°C. At this temperature, one can

expect a current density of

approximately 1.75 A/cm2. The

electrons will have a potential

distribution of 0 to 2 volts. With a bias

voltage between 0 and 500 volts, the

electrons can be accelerated toward

the anode. An SEM image and a

chematic diagram of a tungsten

cathode is shown in the Figures.

(http://www.semitracks.com/reference/FA/die_level/sem/scan_elect.htm).

The Filament & Thermionic Emission

LaB6

As the need for higher resolution

imaging increased, so did the need for

brighter filaments. The most

straightforward method to achieve this

goal is to find a material with a lower

work function Ew. A lower work

function means more electrons at a given

temperature, hence a brighter filament

and higher resolution. Lanthanum

hexaboride, commonly known as LaB6,

has been the best material developed to

date for this application. The LaB6

filament operates at approximately

2125°C, resulting in a brightness on the

order of five times brighter than a

tungsten filament under the same

conditions. LaB6 filaments tend to be an

order of magnitude more expensive than

tungsten filaments. A schematic of the

LaB6 filament is shown in Figure

Electron Lenses

•A strong magnetic field is generated

by passing a current through a set of

windings.

• This field acts as a convex lens,

bringing off axis rays back to focus.

• Focal length can be altered by

changing the strength of the current.

• The image is rotated, to

a degree that depends on the strength

of the lens.

In 1926, Hans Busch discovered

that magnetic fields could act as

lenses by causing electron beams to

converge to a focus. A few years

later, Max Knoll and Ernst Ruska

made the first modern prototype of

an electron microscope

Invention of Scanning Electron Microscope

The first electron microscope prototype was

built in 1931 by the German engineers Ernst

Ruska and Max Knoll. Although this initial

instrument was only capable of magnifying

objects by four hundred times, it demonstrated

the principles of an electron microscope. Two

years later, Ruska constructed an electron

microscope that exceeded the resolution

possible using an optical microscope.

SEM or STEM

Invention of Electron Microscopy

The Nobel Prize in

Physics 1986

Dr. Ernst Ruska

at the University

of Berlin.

My first completed scientific work (1928-9) was concerned

with the mathematical and experimental proof of Busch's

theory of the effect of the magnetic field of a coil of wire

through which an electric current is passed and which is then

used as an electron lens. During the course of this work I

recognised that the focal length of the waves could be

shortened by use of an iron cap. From this discovery the

polschuh lens was developed, a lens which has been used since

then in all magnetic high-resolution electron microscopes.

Further work, conducted together with Dr Knoll, led to the first

construction of an electron microscope in 1931. With this

instrument two of the most important processes for image

reproduction were introduced-the principles of emission and

radiation. In 1933 I was able to put into use an electron

microscope, built by myself, that for the first time gave better

definition than a light microscope. In my Doctoral thesis of

1934 and for my university teaching thesis (1944), both at the

Technical College in Berlin, I investigated the properties of

electron lenses with short focal lengths. (From Autobiography)

Comparison of LM and TEM

LM: (a) Direct observation

of the image; (b) image is

formed by transmitted light

TEM: (a) Video imaging (CRT); (b) image

is formed by transmitted electrons impinging

on phosphor coated screen

Both glass and EM lenses

subject to same distortions and

aberrations

Glass lenses have fixed focal

length, it requires to change

objective lens to change

magnification. We move

objective lens closer to or

farther away from specimen to

focus.

EM lenses to specimen distance

fixed, focal length varied by

varying current through lens

SEM Images of Aunt (courtesy to Shruti Tiwari)

Topography (surface picture) – commonly enhanced by „sputtering‟

(coating) the sample with gold or carbon

SEM – what do we get?

Advantages of Using SEM over LM

• The SEM also produces images of high resolution, closely features can be

examined at a high magnification.

• The combination of higher magnification, larger depth of field, greater

resolution makes the SEM one of the most heavily used instruments

Units of Vacuum: The two main units used to measure pressure (vacuum) are torr and Pascal.

Electrons Need a Vacuum

Vacuum

No scattering

Air

Complete scattering

Atmospheric pressure

(STD) = 760 torr or

1.01x105 Pascal.

One torr = 133.32 Pascal

One Pascal = 0.0075 torr

An excellent vacuum in

the electron microprobe

chamber is 4x10-5 Pa

(which is 3x10 -7 torr)

Scanning Electron Microscope

As an electron travels through the interaction volume, it is said to scatter; that is, lose

energy and change direction with each atomic interaction. Scattering events can be

divided into two general classes:

1. Elastic scattering, in which the electron exchanges little or no energy, but

changes direction;

2. Inelastic scattering, in which the electron exchanges significant, and definite,

amounts energy, but has its direction virtually unchanged. Both types of events

determine the size and shape of the interaction volume. Inelastic scattering events

are responsible for the wide variety of characteristic (i.e., element specific) and

non-specific information, which can be emitted and detected from the specimen.

These include secondary electrons, Augér electrons, characteristic and continuum

x-rays, long-wavelength radiation in the visible, IR and UV spectral range

(cathodoluminescence), lattice vibrations or phonons, and electron oscillations or

plasmons. The inelastic scattering events, because many of them are element

specific, are especially useful in quantitative EPMA. For our purposes, the elastic

scattering events are important in that they (1) produce backscattered electrons

and (2) change the shape of the scattering volume (that is the depth to lateral

scattering spatial ratio).

Scanning Electron Microscope

Elastic scattering occurs when the

energy of the scattered electron is the

same as the energy of the incident

electron, i.e. there is no energy

transferred from the beam into the

specimen. Elastic scattering causes the

beam to diffuse through the sample.

Inelastic scattering results when the

incident electron loses energy in its

interaction with the sample. There are a

number of different processes that

cause this. They include: plasmon

excitation, excitation of conduction

electrons leading to secondary electron

emission, ionization of inner shells,

Bremsstrahlung or Continuum x-Rays,

and excitation of phonons. Inelastic

scattering then, slows the electrons as

they penetrate into the sample.

Electron beam interactions can be

classified into two types of events: elastic

interactions and inelastic interactions.

http://www.semitracks.com/reference/FA/die_level/sem/scan_elect.htm

Interaction of electrons with matter in an electron microscope

•Back scatter electrons – compositional

•Secondary electrons – topography

• X-rays – chemistry

Interaction of Electrons with a thick specimen (SEM)

From:Vick Guo, Introduction to Electron Microscopy and Microanalysis

In theory, a higher voltage should give better resolution because of reduction in

wavelength of the beam of electrons. However, the volume of the interaction

increases with increase accelerating voltage. Therefore, the increase in volume of the

region of interaction results in a decrease in resolution. In practice, balance must be

achieved in selecting the optimum acceleration voltage.

Beam Penetration

•Beam penetration

decreases with Z

•Beam penetration

increases with energy

•Electron range ~

inelastic processes

•Electron scattering

(aspect) ~ elastic

processes

Characteristic

X-rays 2-5 m

Backscatter

electrons 1-2µm

Secondary electrons

~100A-10nm

Backscattered electrons (BSE)

Backscattered electrons (BSE) consist of high-

energy electrons originating in the electron

beam, that are reflected or back-scattered out of

the specimen interaction volume by elastic

scattering interactions with specimen atoms.

Since heavy elements (high atomic number)

backscatter electrons more strongly than light

elements (low atomic number), and thus appear

brighter in the image, BSE are used to detect

contrast between areas with different chemical

compositions. The resolution of the images is limited

by the radius in which the

backscattered electrons are produced;

the resolution is limited to the order of

2×Radius, irrelevant of the diameter

of the incident electron beam. The

intensity of the backscattered electron

signal is also affected by the

composition, in particular any

inhomogeneity, in the sample.

Sketch of backscattered electron detector

Backscatter Electron Detection

A solid-state (semi-conductor) backscattered electron

detector (a) is energized by incident high energy

electrons (~90% E0), wherein electron-hole pairs are

generated and swept to opposite poles by an applied

bias voltage.

In-Lens and Energy Selective BSE

UofO- Geology 619, CAMCOR, UNI Oregon. http://epmalab.uoregon.edu/

BSE detector

Elastic process: Backscattered Electrons

SEM image (Backscattering Electrons) of the single not used ICPG granule

1

2

3

4

Backscattering Electron Imaging: Atomic Number Contrast

Raney Ni-Al

50 m 2 m

Al-Cu eutectic Obsidian

10 m

UofO- Geology 619, CAMCOR, UNI Oregon. http://epmalab.uoregon.edu/

Backscatter arises from interaction of electrons with nucleus: atoms

with higher mass scatter more.

Secondary Electrons

Secondary electrons are defined as those

electrons emitted that have an energy of

less than 50 eV. Secondary electrons come

from the top 1 to 10 nm of material in the

sample, with 1nm being more

characteristic for metals, and 10 nm being

more characteristic for insulators. The

secondary electron coefficient tends to be

insensitive to atomic number. The

secondary electron coefficient is, however,

dependent on beam energy. Starting at

zero energy, the secondary electron

coefficient rises with increasing energy,

reaching unity around 1 keV. The curve

then peaks at just over 1 for metals and as

high as 5 for insulators and then falls

below unity between 2 and 3 keV. This

region above unity tends to be a good

beam energy for performing voltage

contrast.

Atom Structure and Secondary Electrons

The most popular SEM imaging is done by interpreting

secondary electrons. When the electron beam scans the

sample surface, high-energy electrons from the incident

beam interact with valence electrons of the sample

atoms. The valence electrons are released from the atom

and emerge from the surface, often after traveling

through the sample. The emergent electrons with

energies less than 50 eV are called secondary electrons.

Secondary Electron Images

From http://www.jeol.com/PRODUCTS/JEOLProductsResources/ImageGalleries/tabid/351/AlbumID/748-

8/Default.aspx

Comparison of SEM techniques

Top: backscattered electron

analysis - composition

Bottom: secondary electron

analysis - topography

Secondary Electron Production

Pollen

SE imaging: the signal is from the top 5

nm in metals, and the top 50 nm in

insulators. Thus, fine scale surface

features are imaged. The detector is

located to one side, so there is a shadow

effect – one side is brighter than the

opposite.

Detection :Electrons Scintillator

photons photomultiplier conversion

into electric current detection

SE detector

Resolution Limits Imposed by Spherical Aberration, Cs

For Cs > 0, rays far from the axis are bent too strongly and come to a crossover

before the gaussian image plane (focus).

For a lens with aperture angle α, the minimum blur is

min d

Typical TEM numbers: Cs= 1 mm, α=10 mrad → dmin= 0.5 nm

3

min2

1sCd

Spherical aberration is the failure of the lens system to image central and peripheral

electrons at the same focal point.

Resolution Limits Imposed by Spherical Aberration, Cs

A diatom imaged using different working distances. At a longer working distance (WD =

48mm) spherical aberration is present decreasing resolution (A). At a shorter working

distance (WD = 8) the effect of spherical aberration is less resulting in an image with

improved resolution (B). Bar is 5µm, Magnification = x 3300, Acceleration Voltage =

5kV, Condenser Lens setting = 14 (A and B).

http://131.229.114.77/microscopy/semvar.html

Evaluation, at electron wavelengths (e.g., 0.0037 nm at 100 kV), of the expressions for

limiting resolving power would appear to suggest the possibility of electron- optical

resolutions beyond 0.001 nm. However, several other factors must be con sidered in

electron microscopy. In particular, spherical aberration, which can be reduced to negligible

levels in glass lenses, remains significant even in the best electron lenses. Feasible aperture

angles are therefore small (<10-2 rad), so that the “sin = ” approximation is valid, giving

as a general expression for the resolving power of an electron lens.

A first approximation to estimation of attainable resolving power equates the radius of

the diffraction figure to the radius of the disc of confusion due to spherical aberration.

Ignoring numerical constants, this gives the optimal aperture angle as (/C)1/4 and

yields, by substitution in eq. (1),

Balancing Spherical Aberration against the Diffraction Limit

min min2d r

(1)

1/ 4 3/ 4

min sd C

where Cs is the spherical aberration constant. This equation predicts ultimate resolving

powers, at 100 kV, on the order of 0.5 nm (E. Slayter, Light and Electron Microscopy).

SE and BSE Images

SE

20kV

SE

5kV

BSE

BSE

Grains in a Polished Fe-Si Alloy by Different SEM methods

David Muller 2008, Cornel University

5 kV 25 kV

kV and Fine Structure

From: UofO- Geology 619

Depth of Focus

By simply shortening the working distance the background is blurred drawing the viewers eye to the bugs proboscis.

SEM Example

A diatom imaged using different accelerating voltages. Fine detail of a diatom

imaged at a low accelerating voltage of 5kV is visible (A). A decrease in resolution

and contrast can be observed when a diatom is imaged using a much higher

accelerating voltage (20kV) (B). Bar is 1µm, Magnification = x 4000, Working

Distance = 8mm, Condenser Lens setting = 15 (A and B).

These backscattered electrons may generate

secondary electrons near the sample surface

on their way out, increasing the area from

which secondary electrons are produced

and therefore reducing the resolution of the

final image.

X-ray Generation and Detection

Resolution in SEM and TEM

The spatial resolution of the SEM depends on the size of the electron spot, which in

turn depends on both the wavelength of the electrons and the electron-optical system

which produces the scanning beam. The resolution is also limited by the size of the

interaction volume, or the extent to which the material interacts with the electron

beam. The spot size and the interaction volume are both large compared to the

distances between atoms, so the resolution of the SEM is not high enough to image

individual atoms, as is possible in the shorter wavelength (i.e. higher energy) (TEM).

Depending on the instrument, the resolution can fall somewhere between less than

1 nm and 20 nm. By 2009, The world's highest SEM resolution at high beam

energies (0.4 nm at 30 kV) is obtained with the Hitachi S-5500.

In a TEM, a monochromatic beam of electrons is accelerated through a potential of

40 to 100 kilovolts (kV) and passed through a strong magnetic field that acts as a

lens. The resolution of a modern TEM is about 0.2 nm. This is the typical separation

between two atoms in a solid. This resolution is 1,000 times greater than a light

microscope and about 500,000 times greater than that of a human eye.

Magnification in Scanning Electron Microscopy

Magnification in a SEM can be controlled over a range of up to 6 orders of

magnitude from about 10 to 500,000 times. Unlike optical and transmission

electron microscopes, image magnification in the SEM is not a function of the

power of the objective lens. SEMs may have condenser and objective lenses, but

their function is to focus the beam to a spot, and not to image the specimen.

Provided the electron gun can generate a beam with sufficiently small diameter, a

SEM could in principle work entirely without condenser or objective lenses,

although it might not be very versatile or achieve very high resolution. In a SEM,

as in scanning probe microscopy, magnification results from the ratio of the

dimensions of the raster on the specimen and the raster on the display device.

Assuming that the display screen has a fixed size, higher magnification results

from reducing the size of the raster on the specimen, and vice versa.

Magnification is therefore controlled by the current supplied to the x, y scanning

coils, or the voltage supplied to the x, y deflector plates, and not by objective lens

power.

Home Work

1. Describe the Principle of Scanning Electron(SO).

2. Derive Lateral resolution of SEM (KK).

3. Provide a definition of Backscattering Electrons. Explain the contrast of SEM image

obtained by backscattered electrons (SO).

4. Provide a definition of Secondary Electrons. Explain the contrast of SEM image

obtained by secondary electrons (KK).

5. Estimate the maximal resolution and magnification of SEM (KK).